Open Collections

$G_2$ Laplacian flow and higher codimensional spacelike mean curvature flow

Banff International Research Station for Mathematical Innovation and Discovery

It is known that higher codimensional mean curvature flow appears naturally in the $G_2$-Laplacian flow of coassociative fibrations. With this motivation, we consider entire higher codimensional mean curvature flow in $\mathbb R^{n,m}$ of $n$-dimensional spacelike manifolds and prove a long time existence theorem starting from arbitrary spacelike initial data. We will see that the key to the proof is to demonstrate local spacelike gradient estimates, and to get around difficulties with cutoff functions in $\mathbb R^{n,m}$. This yields new long time existence results for the $G_2$-Laplacian flow.

Mathematics; Differential geometry; Geometry

video/mp4

Author affiliation: University College London

2019-11-04

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/72180

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/